When AI systems make errors in high-stakes domains like medical diagnosis or autonomous vehicles, a single algorithmic flaw across varying operational contexts can generate highly heterogeneous losses that challenge traditional insurance assumptions. Algorithmic insurance constitutes a novel form of financial coverage for AI-induced damages, representing an emerging market that addresses algorithm-driven liability. However, insurers currently struggle to price these risks, while AI developers lack rigorous frameworks connecting system design with financial liability exposure. We analyze the connection between operational choices of binary classification performance to tail risk exposure. Using conditional value-at-risk (CVaR) to capture extreme losses, we prove that established approaches like maximizing accuracy can significantly increase worst-case losses compared to tail risk optimization, with penalties growing quadratically as thresholds deviate from optimal. We then propose a liability insurance contract structure that mandates risk-aware classification thresholds and characterize the conditions under which it creates value for AI providers. Our analysis extends to degrading model performance and human oversight scenarios. We validate our findings through a mammography case study, demonstrating that CVaR-optimal thresholds reduce tail risk up to 13-fold compared to accuracy maximization. This risk reduction enables insurance contracts to create 14-16% gains for well-calibrated firms, while poorly calibrated firms benefit up to 65% through risk transfer, mandatory recalibration, and regulatory capital relief. Unlike traditional insurance that merely transfers risk, algorithmic insurance can function as both a financial instrument and an operational governance mechanism, simultaneously enabling efficient risk transfer while improving AI safety.

翻译：当人工智能系统在医疗诊断或自动驾驶等高风险领域犯错时，一个算法缺陷在不同操作环境下可能产生高度异质性的损失，这挑战了传统保险的基本假设。算法保险构成了一种针对AI引发损害的新型金融保障形式，代表着应对算法驱动责任的新兴市场。然而，保险公司目前难以对这些风险进行定价，而AI开发者缺乏将系统设计与金融责任敞口联系起来的完整框架。我们分析了二分类性能的操作选择与尾部风险敞口之间的关联。通过使用条件风险价值（CVaR）来捕捉极端损失，我们证明与尾部风险优化相比，最大化准确率等传统方法会显著增加最坏情况下的损失，且随着阈值偏离最优值，惩罚呈二次方增长。随后我们提出了一种强制性风险感知分类阈值的责任保险合同结构，并刻画了该结构为AI提供商创造价值的条件。我们的分析扩展到了模型性能退化和人工监督场景。我们通过乳腺癌钼靶诊断案例研究验证了研究发现，证明CVaR最优阈值相比准确率最大化可将尾部风险降低高达13倍。这种风险降低使得保险合同能够为校准良好的公司创造14-16%的收益，而校准不良的公司通过风险转移、强制重新校准和监管资本减免可获得高达65%的收益。与仅转移风险的传统保险不同，算法保险既可以作为金融工具，也可以作为运营治理机制，在实现高效风险转移的同时提升AI安全性。